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Find the equation of the parabola that satisfies the given conditions: Focus $(6,0)$ and Directrix $x=-6$

$\begin{array}{1 1}y^2 = 24x \\ y^2 =- 24x \\x^2 = 24y \\ x^2 = -24y \end{array} $

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Given Focus $(6,0)$ and Directrix $x=-6$
Since the Focus is on the x-axis $\rightarrow$ this is the axis of the parabola.
The Directrix is to the left of the y-axis, while the Focus is on the right.
Therefore, this is of the type $y^2=4ax$ where $a = 6$
Therefore the equation of the parabola is $y = 4 \times 6 \ x = 24x$
answered Apr 1, 2014 by balaji.thirumalai

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